Question

monotocity of a positive martingale

score 44 · Answer 1 · 2026-04-11 01:43:41

44

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monotocity of a positive martingale

Published on 11 Apr 2026 - 1:43

score 72 · Answer 2 · 2026-04-12 12:34:30

72

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Interpretation of Stopped $\sigma$-algebra

Published on 12 Apr 2026 - 12:34

score 60 · Answer 3 · 2026-04-12 16:46:21

60

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Probability that a 2d SRW starting from $x$ hits $\partial B_n$ before hitting $0$

Published on 12 Apr 2026 - 16:46

score 46 · Answer 4 · 2026-04-12 18:15:45

46

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Martingale with respect to different filtration

Published on 12 Apr 2026 - 18:15

score 294 · Answer 5 · 2026-04-03 10:52:04

294

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Show that $\mathbb E[\exp(-\lambda(T_{a}\land T_{b}))]=\cosh(\frac{a+b}{2}\sqrt{2\lambda})/\cosh(\frac{a-b}{2}\sqrt{2\lambda})$

Published on 03 Apr 2026 - 10:52

score 287 · Answer 6 · 2026-04-11 05:26:29

287

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Showing that a martingale $Y_k$ does not converge almost surely.

Published on 11 Apr 2026 - 5:26

score 337 · Answer 7 · 2026-04-12 06:50:24

337

Views

Almost sure convergence, uniformly integrable and L1 convergence

Published on 12 Apr 2026 - 6:50

score 63 · Answer 8 · 2026-04-06 14:21:24

63

Views

Why would $\mathbb P( S > x \lvert \mathcal{F}_{0})= \frac{X_{0}}{x}\land 1$ imply that $S$ is distributed under $\mathcal F_{0}$ as $X_{0}/U$

Published on 06 Apr 2026 - 14:21

score 33 · Answer 9 · 2026-04-11 22:33:01

33

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Is it possible to recover the fact that $\mathbb P(T_{a} < T_{b} ) = b/(b-a)$ using $\mathbb E[ e^{-\lambda T_{a}}\chi_{\{T_{a}< T_{b}\}}]$

Published on 11 Apr 2026 - 22:33

score 68 · Answer 10 · 2026-04-07 02:08:03

68

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L2 bound of a submartingale

Published on 07 Apr 2026 - 2:08

score 211 · Answer 11 · 2026-04-12 12:27:42

211

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Proof Reference For Doob's First Stopping Time Theorem

Published on 12 Apr 2026 - 12:27

score 377 · Answer 12 · 2021-11-10 22:35:45

377

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I know that $\exp(\lambda B_{t} -\frac{\lambda^{2}}{2}t)$ is a martingale, how can I use it to prove that the following are martingales

Published on 10 Nov 2021 - 22:35

score 38 · Answer 13 · 2021-11-13 18:39:05

38

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Show that $\mathbb E [B_{t} - B_{s} \lvert \mathcal{G}_{s}]=\frac{t-s}{1-s} (B_{1}-B_{s})$

Published on 13 Nov 2021 - 18:39

score 122 · Answer 14 · 2021-11-14 14:10:29

122

Views

An application of the martingal convergence theorem on a special product of i.i.d. uniformly distributed random variables

Published on 14 Nov 2021 - 14:10

score 236 · Answer 15 · 2021-11-15 12:10:42

236

Views

Sum of Product of Martingale and its difference

Published on 15 Nov 2021 - 12:10

List Question

monotocity of a positive martingale

Interpretation of Stopped $\sigma$-algebra

Probability that a 2d SRW starting from $x$ hits $\partial B_n$ before hitting $0$

Martingale with respect to different filtration

Show that $\mathbb E[\exp(-\lambda(T_{a}\land T_{b}))]=\cosh(\frac{a+b}{2}\sqrt{2\lambda})/\cosh(\frac{a-b}{2}\sqrt{2\lambda})$

Showing that a martingale $Y_k$ does not converge almost surely.

Almost sure convergence, uniformly integrable and L1 convergence

Why would $\mathbb P( S > x \lvert \mathcal{F}_{0})= \frac{X_{0}}{x}\land 1$ imply that $S$ is distributed under $\mathcal F_{0}$ as $X_{0}/U$

Is it possible to recover the fact that $\mathbb P(T_{a} < T_{b} ) = b/(b-a)$ using $\mathbb E[ e^{-\lambda T_{a}}\chi_{\{T_{a}< T_{b}\}}]$

L2 bound of a submartingale

Proof Reference For Doob's First Stopping Time Theorem

I know that $\exp(\lambda B_{t} -\frac{\lambda^{2}}{2}t)$ is a martingale, how can I use it to prove that the following are martingales

Show that $\mathbb E [B_{t} - B_{s} \lvert \mathcal{G}_{s}]=\frac{t-s}{1-s} (B_{1}-B_{s})$

An application of the martingal convergence theorem on a special product of i.i.d. uniformly distributed random variables

Sum of Product of Martingale and its difference

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